Non-equilibrium topological phenomena can be induced in quantum many-body systems
using time-periodic fields (for example, by laser or microwave illumination). This Review …

There have been significant recent advances in realizing band structures with geometrical
and topological features in experiments on cold atomic gases. This review summarizes …

Time-periodic forcing in the form of coherent radiation is a standard tool for the coherent
manipulation of small quantum systems like single atoms. In the last years, periodic driving …

Since the discovery of topological insulators, many topological phases have been predicted
and realized in a range of different systems, providing both fascinating physics and exciting …

Photonic synthetic materials provide an opportunity to explore the role of microscopic
quantum phenomena in determining macroscopic material properties. There are, however …

This is an introductory review of the physics of topological quantum matter with cold atoms.
Topological quantum phases, originally discovered and investigated in condensed matter …

Driving a quantum system periodically in time can profoundly alter its long-time dynamics
and trigger topological order. Such schemes are particularly promising for generating …

Sixty years ago, Karplus and Luttinger pointed out that quantum particles moving on a lattice
could acquire an anomalous transverse velocity in response to a force, providing an …

Fractional quantum Hall (FQH) states are known for their robust topological order and
possess properties that are appealing for applications in fault-tolerant quantum computing …

We demonstrate the experimental implementation of an optical lattice that allows for the
generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms …